MPSKM Algorithm to Cluster Uneven Dimensional Time Series Subspace Data

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 686
MPSKM ALGORITHM TO CLUSTER UNEVEN DIMENSIONAL TIME SERIES
SUBSPACE DATA
S. Gokila1 , Dr. K. AanandaKumar2 , Dr. A. Bharathi3
1Research Scholar, Bharathiar University, India,
2Asst. Professor (SG), Department of Computer Science and Engineering,
Bannari Amman Institute of Technology, India,
3Professor, Department of Information Technology,
Bannari Amman Institute of Technology, India, bharathia@bitsathy.ac.in
-------------------------------------------------------------------------***--------------------------------------------------------------------------
Abstract: The objective of the proposed algorithm is to select
the attribute’s rank index based on the involvements of the
same in data set; identifying the global and local outline of
entire data set. Because the attributes in data set, number of
cluster and outline object are major intervention decide the
accuracy of each clusters. The attribute ranking of proposed
method automate the number of clusters and the center of the
cluster. The uniqueness of the algorithm is exhibited in
maintaining complete set of attributes without eliminating
the low ranked attribute which are required for predictive
analysis and in grouping the outline data set as clusters. The
dynamited and improved version of MPSKM algorithm
reduces the Sum of Square Error and number of iteration in
cluster formation. The work shows the significant reduction in
number of iteration in cluster formation and identifying the
outline in data set based on rank index technique. The
algorithm very well suited for the data set required periodical
analysis and influences of attribute varies in each period of
subset. The algorithm applied and tested on four years of
Weather data set.
Keywords: Data Mining, Outline, Extreme, Automated Mean,
Projected Space, Weather Season
1. INTRODUCTION
Data mining process is dominated decision support process
on the business application according to the available data
and the prediction approach. Clustering is one of the major
areas in data mining to group similar pattern under one
label. The data are formed under specific group based on
the similarity among those object. There are many
methodologies proposed to find the similarity among the
objects. This labeling is called as unsupervised mining. The
key notes decides the accuracy of cluster are attributes
involved, number of clusters decided and the similarity
threshold fixed.
Outlines are the object that dissimilar from other data points
among data set. It is an important task of finding such
outliner in many application like, stock market, fraud
detection and weather forecasting. In clustering outliners
are considered as separate group of data to retain the
sensitivity of other groups. The proposed method handles
attribute selection, inclusion of all the attributes based on
rank index, number of cluster and dissimilarity thresholds.
The attributes are selected based on the projected space
algorithms, number of clusters are decided based on the
proximity of data in the state space.
1.1 Attribute Ranking
Clusters of same data set may differ in dimension. One
cluster may have an object with similar data in some
dimension. Other cluster may have object with similar data
with other set of dimension. But there is need of comparing
these differential clusters[15]. Some of the projected space
clustering filter less important dimension from the chosen
set of attributes[3, 17]. Treat that as less in cluster formation
and eliminate those dimensions. The clustering done with
the remaining data set. The dimension removed as may
influence as predicator in classification in some domain like
weather and stock market[1, 8].
So the attributes are major inducer of cluster
accuracy. There are some clustering algorithms where the
attribute plays major role in clustering. The algorithm
CACTUS starts from initial core attribute which is not
allowed to appear on another cluster[4]. The algorithm
COOLCAT use entropy to calculate the closeness of
clusters[2]. It needs the K input to select centroid of clusters.
The CLICK used graph based partition of data by applying
weighted attributes[17]. The attributes are vertex of graph
the edge between the vertexes weighted to find the
proximity of the vertexes. This will not handled high
dimension data. The algorithm PROCAD projects the weight

based attributes and rejects the low rank attributes and this
works only for categorical data set alone[10]. The method
proposed in this paper find the attributes by comparing pair
of ratio among attributes and form a rank matrix, from
which attributes are ranked. These variable selection allows
to add the new variable and also decides the number of
clusters.
1.2 Outline Detection
An outlier is an observation that deviates from other
observations as to arouse suspicions that it was generated
by a different mechanism and is also defined as a noisy
observation that does not fit to the assumed model that
generated the data[6, 17]. It is an important task of finding
such outliner in many applications like, stock market, fraud
detection and weather forecasting. There are many
approaches in finding outline: Mahalanobis distance, depth-
based approaches, deviation-based approaches, distance-
based approaches, density-based approaches and clustering-
based[12]. All these approaches are based nature on the
user input. Outliers can be categorized as global and local
outliers. Global outliers are completely isolated and grouped
into separate cluster. Local outline create inconsistency with
neighbor objects. The present work identifies the outline
object and forms that as separate cluster which supports for
high accuracy in other clusters.
1.3 Clustering
Cluster analysis is to explore the structure of data. Core
Cluster analysis is a clustering. Clustering analysis in a data
is an unknown label class (unsupervised)[5, 9]. So it is
learned by observation not learned by example[11].
Clustering divide the data set into classes using the principle
of “Maximum intra class similarity and Minimum inter class
similarity”.
It doesn’t have any assumption about the category of
data. The basic clustering techniques are Hierarchical,
Partitioned, Density based, Grid based and Model based
clustering[7]. Some sort of measure that can determine
whether two objects are similar or dissimilar is required to
add them into particular class. The distance measuring type
varies for different attribute type. Clustering can also be
used to detect outline in data which may occur due to
human error or some abnormal events occurred while
creating data set[9, 11]. Cluster work well on scalable,
heterogeneous and high dimensional data set. In all the
clustering algorithms user defined parameters are given as
input to find either similarity, dissimilarity among clusters
and for root attribute of cluster and for maximum or
minimum number of clusters.
2. METHODS AND MODEL
The MPSKM model suggested here work well on domains
examination result analysis, stock value analysis which are
the fields required seasonal study or some periodical
analysis. The Model derives 1 to N seasons of data. The
MPSKM model starts with cluster formation of each slice of
data based on the patterns exist, from which the extreme
event fall on separated cluster. In traditional clustering
algorithm the prefixed set of clusters include the extreme
event of data which affect the statistical values (mean,
centroid, etc.) of the cluster. The notation used in algorithm
are described in [Table 1 ]
Clusters of same data set may differ in dimension. One
cluster may have an object with similar data in some
dimension. Other cluster may have object with similar data
with other set of dimension. First phase of proposed model
starts with find a attribute which close related to cluster for
N slice(s) of data. Along the attribute finding the number of
cluster K of N set also predicted.
The algorithm finds the rank matrix for D(D-1)/n pair of
domain based on sum of square error values. With the same
it decides the optimum number of K cluster and initial
center point M of K clusters. The dimension of data set are
transformed based on the RM order of respective D. The
algorithm steps are represented in [Fig : 1].
Table 1 : Algorithms notation
Notation Description
D No of Dimension (Attribute)
RM Rank Matrix
S Standard Deviation
H Euclidean Error of D
n Number of objects
N Number of slices of data
K Number of Clusters
Ckn Set of clusters of N
Mk Midpoint of Ck
The proposed version finds the K using rank index
based on the probability distribution of D={d1,d2....di}
1. Compute RM for pair of D(D-1)/2 attributes.
2. Find ∑ ∑

3. Number of cluster of Nth Slice K= Count(hj+1> hj +
Sj)
4. Sort the RM based on the H
5. Rank D= {d1, d2, d3, … dj} X Max(RM)
6. Choose Mk the midpoints of K Clusters.
7. Use the objective function ∑ ∑
assign Xj into closest Ck
8. Refine Mk for all Ck cluster.
9. Repeat 7 and 8 until no more changes in Mk.
Figure 1 : MPSKM work flow
The rank index formation makes the clustering effective by
deciding the number of cluster, importance of each attribute
in cluster and also outline identification. The rank matrix
formed using f(D) in which the entire attribute are studied
using proximity of values individually by the probability
mapping Eqn (1).
p( hj+ di (xi,mid (Di))) Eqn (1)
The ordered probability decides the rank of attribute. The
higher order probability attributes are the base to decide K
and also the Ci. The Min(RM) find the outline in lower end
and also the labels the attribute which is the root cause of
the event. All these preliminary works considerably reduces
the cluster refinement. The objects allocation to the clusters
are decided at the earliest. The proposed method is the
latest version of MPSCM which induce the soft cluster
formation with individual attribute threshold based on the K
equal to dimension in state space[14]. The number of
clusters are limited using the Eqn (2).
hj+1 > hj + Sj Eqn (2)
3. RESULT ANALYSIS
3.1. Data Set
The Performance of MPSKM evaluated by applying on
weather date set. Four years (2010,2011,2012 and 2013) of
weather date in 11.0o latitude and 76.9o longitude is taken
for analysis. Indian weather are classified into four seasons
each one belongs to separate sub space of data and in each
slice of data importance of same set of attribute varies. In
summer season Temperature attribute are considered along
with the wind, at the same time the variation in rain
indicates the extreme event. So the weather domain has
been chosen to study the performance of MPSKM algorithm.
This kind of study is required because the Indian weather
seasons are classified into four and each of the seasons the
importance of attribute varies[13,16]. The dimension of data
set includes TemperatureMin, TemperatureMax, Rain,
Humidity, Wind Speed, Radiation, and Evaporation (D=7).
All the attributes are of numerical type. Number of objects
in each data set are 1460(n).
3.2 Generating Rank Index
The attributes in the data set carry different level of
importance when the same data set fragmented into various
parts. This is applicable when the fragments are of unequal
in size. So it is important to identify the level of involvement
of attributes in each set separately. The same set of work is
the projection on the dimensions. Some of the projection
algorithms excludes the low level of attributes in the final
stage of preprocessing. The low rated attributes many also
contains the sensitive data and supports to identify the
outline are extreme data set. The MPSKM identifies the
ranking and it converges the attributes with consistent
weight based on the level of importance. The algorithm runs
the T-State K-Mean on D dimensional data set. It generates
the D(D-1)/2 pair wise matrix to generate the rank matrix.
Result of which find the minimum sum of square error in
heuristic fusion using the level Eqn 2.This limitation
equation identify the number of clusters. The ratio of
difference between the each pair of sum of square and the
total sum of square of the data base sorts the entire domain
propositional the error rate. The RM for experimental data
set is in the Table 2.
Data
Set Slic
e
Sea
son
al
Rank
Base
Weig
ht
Identi
fy
Numb
er of
Clust
ers
MPS
Clus
ter
Rank
Inde
x
Dim
ensio

Table 2: RM of four years data set.
D/j Sub
Space
D1 D2 D3 D4 D5 D6 D7
DS1
N1 2 7 5 1 3 3 6
N2 4 6 7 3 1 2 5
N3 3 6 5 2 4 4 1
N4 4 3 1 3 2 5 7
DS2
N1 2 7 5 1 3 3 6
N2 4 6 7 3 1 2 5
N3 3 6 5 2 7 4 1
N4 4 3 1 3 2 5 7
DS3
N1 2 7 5 1 3 3 6
N2 4 6 7 3 1 2 5
N3 3 6 5 2 4 4 1
N4 4 3 1 3 2 5 7
DS4
N1 2 7 5 1 6 3 6
N2 4 6 7 3 1 2 5
N3 3 6 5 2 4 4 1
N4 4 3 1 3 2 5 7
The RM states the different levels of involvement of same
attribute in different sub space. The variation in the
attribute occurs because of the extreme in particular sub
space. In the attributes (D5,D6) occurs DS1(N1) ≈ DS4(N1)
due to the extreme in DS4 that show in Fig 4. Weight
application on the rank matrix done as W(RM) = Maxj
(RMj)*∂. Scaling transformation are applied on the actual
data set using is weighted matrix. Along with the RM the K
value of each N1 to N4 also identified.
3.3 Cluster Validity
The model implemented in RStudio the open source
data analysis tool. All the four sets of data are preprocessed
and synthesized and formatted as CSV file after receiving it
from different sources. Based on the nature of domain model
receives input from the user to slice the data into N number
of parts. Here the data taken for study is Indian weather
data, as Indian weather is naturally of four seasons each data
set are sliced into 4 groups and given as input to the
model[13]. In the analysis each year of state space are
referred as DS1, DS2, DS3, DS4. The sub space {N1,
N2,N3,N4} ⊆ DS1 the state space. For each slice N1,N2,N3
and N4 model predicts the number of clusters and the
importance of attributes based on the rank index matrix. It
gives different ranks for the same attribute in each slice of
data based on the nature of value, variation of value and
outline event caused.
Each slice produces different set of cluster which is decided
by the model based on the number pair of Euclidian error
and mean value balance in each attribute. The data set taken
for the study projected with 6 attributes, all are with
different importance in each slice, for example the
temperature in summer definitely high when compare to
summer season, so the cluster of such data have to be taken
place within the data of same season and the importance of
such attribute are decided using rank matrix and the same
allied as |w1,w2….wj|{d1,d2…dj} .
Even with in the season the range of each attribute vary, that
the distance calculation with centroid using traditional
method may leady the cluster quality to low. So the distance
measured among relevant attribute yield considerable
quality improvement in cluster. The number of clusters of
each slice in object predicted in rank index formation that
reduces the clustering iteration and the same improves the
sum of square error within each clusters. The outcome of
MPSKM algorithm compared with previous version of
algorithm that K-Mean algorithm. The compression results
represented in [Table 3, 4, 5, 6].
Table 3 : MPSKM – K Mean in DS1
MPSKM K- Mean
Data
Set
N Ck No of
Iteration
SEE No of
Iteration
SEE
DS1
N1 4 4 92.3 7 95.4
N2 5 4 92 6 93.5
N3 4 4 93.4 5 95.2
N4 6 5 91.8 6 92.7
MPSKM K- Mean
Data
Set
N Ck No of
Iteration
SEE No of
Iteration
SEE
DS2
N1 5 4 91.7 7 93.4
N2 6 4 92.1 6 93.6
N3 4 3 91.2 5 92.5
N4 5 4 90.2 6 91.7
Clustering divide the data set into classes using the principle
of “Maximum intra class similarity and Minimum inter class
similarity”. The SSE applied to validate the similarity of
objects with in the cluster.

MPSKM K- Mean
Data
Set
N Ck No of
Iteration
SEE No of
Iteration
SEE
DS3
N1 5 3 90.2 7 91.7
N2 5 4 91.1 6 92.2
N3 6 4 92.4 7 93.1
N4 4 4 90.5 5 91
The rank based attributes of the model the SSE of final
formation of cluster doesn’t have more deviation from the
SSE of cluster formed in initial clustering iteration and at the
same SSE is less when compare to the SSE of K-Mean Mean
algorithm.
MPSKM K- Mean
Data
Set
N Ck No of
Iteration
SEE No of
Iteration
SEE
DS4
N1 5 4 91.2 7 92.5
N2 4 4 91 5 91.4
N3 5 4 91.5 6 93.4
N4 6 5 91 6 92.1
Due to the existance of outline the k-mean show the more
iteration for cluster refinement the same has been reduced
in MPSKM as it notifies the outline. The clusters formed in
proposed model highlight the outline objects with respect to
the attribute changes. Those clusters are shown in [Fig 3 and
Fig 4]. Extreme occurrences of object in each slice of data are
clustered separately. DS1 slice of 2013 data with extreme
rainfall object and wind object are ensemble clearly. These
two extremes are of different attributes that are clustered in
C13 and C14 for Rain and Wind respectively. N4 slice of same
year data consist two extreme objects for Rainfall. That are
ensemble in single cluster C43.
Figure 2: Cluster Iteration Comparision of MPSKM and K-Mean
Compare to the traditional K Means algorithm, the MPSKM
performs better in reduction of clustering iterations which
is obviously proportional to run time of algorithm .
Running time of the algorithm is proportional to the
volume of the data but the complexity of it less compare to
the other methods.

Figure 3: N1 – DS4 outline Pattern
The less computational complexity relate with the
iteration of cluster in which the object reallocation
considerably minimum compare to K-mean. Iteration and
Sum of square error comparison are show in [Fig 2]. So
the number of scan in state space considerably minimized.
Figure 4: N4 – DS4 outline Pattern
4. CONCLUSION
The major challenge of unsupervised clustering are
deciding new latent variable that is possible by ensemble
of closed data, Deciding possible values in latent variable
and outline data. The closeness of data point get deviated
with the existence of outline data. In proposed method the
event based actual outline are grouped under new label
along with the relevant attribute. The MPSKM model solve
handles unequal attribute and to identify the extreme
(low/ high) event and deciding the number of K value to
group the date point with closest center. Proposed method
finds the K value simultaneously with the rank matrix. The
rank matrix transforms the original data point with the
weight to increase the cluster accuracy. All of these reduce
the number of iteration in finalizing the data point
allocation and sum of square error among the clusters. The
method achieves the soft clustering where the data point
belongs to the exact label with reasonable attributes
changes. The enhancement of the work direct to the
pattern on weather data after identifying the outline and
rank based on MPSKM algorithm. It supports to study the
data set in different sub space along with various
involvement of the attributes.
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MPSKM Algorithm to Cluster Uneven Dimensional Time Series Subspace Data

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